To complement recent articles in this journal on structural equation modeling (SEM) practice and principles by Martens and by Quintana and Maxwell, respectively, the authors offer a consumer’s guide to SEM. Using an example derived from theory and research on vocational psychology, the authors outline six steps in SEM: model specification, identification, data preparation and screening, estimation, evaluation of fit, and modification. In addition, the authors summarize the debates surrounding some aspects of SEM (e.g., acceptable sample size, fit indices), with recommendations for application. They also discuss the need for considering and testing alternative models and present an example, with details on determining whether alternative models result in a significant improvement in fit to the observed data.
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References
1.
Allison, P. D. (2003). Missing data techniques for structural equation modeling. Journal of Abnormal Psychology, 112, 545-557.
2.
Anderson, J. C., & Gerbing, D. W. (1984). The effects of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49, 155-173.
3.
Anderson, J. C., & Gerbing, D. C. (1988). Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, 103, 411-423.
4.
Arbuckle, J. L. (2003). Amos user’s guide. Chicago: SmallWaters.
5.
Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182.
6.
Bentler, P. M. (1995). EQS structural equations program manual. Encino, CA: Multivariate Software.
7.
Bentler, P. M. (1990). Comparative fit indices in structural models. Psychological Bulletin, 107, 238-246.
8.
Bollen, K. A. (1989). A new incremental fit index for general structural equation models. Sociological Methods & Research, 17, 303-316.
9.
Bollen, K. A., & Long, J. S. (Eds.). (1993). Testing structural equation models. Newbury Park, CA: Sage.
10.
Boomsma, A. (2000). Reporting analyses of covariance structures. Structural Equation Modeling, 7, 461-483.
11.
Browne, M. W., & Cudek, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: Sage.
12.
Byrne, B. M. (2001). Structural equation modeling with AMOS: Basic concepts, applications, and programming. Mahwah, NJ: Lawrence Erlbaum.
13.
Campbell, D. P., Hyne, S. A., & Nilsen, D. L. (1992). Manual for the Campbell Interest and Skills Inventory. Minneapolis, MN: National Computer Systems.
14.
Chou, C.-P., & Bentler, P. M. (1990). Model modification in covariance structure modeling: A comparison among the likelihood ratio, Lagrange Multiplier, and Wald tests. Multivariate Behavioral Research, 25, 115-136.
15.
Chou, C.-P., & Bentler, P. M. (1995). Estimates and tests in structural equation modeling. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues and applications (pp. 37-55). Thousand Oaks, CA: Sage.
16.
Fassinger, R. E. (1987). Use of structural equation modeling in counseling psychology research. Journal of Counseling Psychology, 34, 425-436.
17.
Geurts, S. A. E., Kompier, M. A. J., Roxburgh, S., & Houtman, I. L. D. (2003). Does work-home interference mediate the relationship between workload and well-being? Journal of Vocational Behavior, 63, 532-559.
18.
Green, S. B., Thompson, M. S., & Babyak, M. A. (1998). A Monte Carlo investigation of methods for controlling Type I errors with specification searches in structural equation modeling. Multivariate Behavioral Research, 33, 365-383.
19.
Harmon, L. W., Hansen, J. I. C., Borgen, F. H., & Hammer, A. L. (1994). Strong interest inventory: Applications and technical guide. Palo Alto, CA: Consulting Psychologists Press.
20.
Hartmann, W. M. (1992). The CALIS procedure: Extended user’s guide. Cary, NC: SAS Institute.
21.
Helms, J. E., Henze, K. T., Sass, T. L., & Mifsud, V. A. (2006). Treating Cronbach’s alpha reliability as data in counseling research. The Counseling Psychologist, 34, 630-660.
22.
Henson, R. K. (2006). Effect-size measures and meta-analytic thinking in counseling psychology research. The Counseling Psychologist, 34, 601-629.
23.
Heppner, P. P., Pretorious, T. B., Wei, M., Lee, D., & Wang, Y. (2002). Examining the generalizability of problem-solving appraisal in Black South Africans. Journal of Counseling Psychology, 49, 484-498.
24.
Holland, J. L. (1997). Making vocational choices: A theory of vocational personalities and work environments (3rd ed.). Odessa, FL: Psychological Assessment Resources.
25.
Holland, J. L., Fritzsche, B. A., & Powell, A. B. (1994). Technical manual for the self-directed search. Odessa, FL: Psychological Assessment Resources.
26.
Hoyt, W. T., Warbasse, R. E., & Chu, E. Y. (in press [TCP special issue, part 2]). Construct validation in counseling psychology research. The Counseling Psychologist, 34.
27.
Hoyle, R. H. (Ed.). (1995). Structural equation modeling: Concepts, issues and applications. Thousand Oaks, CA: Sage.
28.
Hoyle, R. H., & Panter, A. T. (1995). Writing about structural equation models. In R. H. Hoyle (Ed.), Structural equation modeling (pp. 158-176). Thousand Oaks, CA: Sage.
29.
Hu, L.-T., & Bentler, P. M. (1995). Evaluating model fit. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues and applications (pp. 76-99). Thousand Oaks, CA: Sage.
30.
Hu, L.-T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424-453.
31.
Hu, L.-T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.
32.
Jackson, D. L. (2001). Sample size and number of parameter estimates in maximum likelihood confirmatory factor analysis: A Monte Carlo investigation. Structural Equation Modeling, 8, 205-223.
33.
Jackson, D. L. (2003). Revisiting sample size and number of parameter estimates: Some support for the N: q hypothesis. Structural Equation Modeling, 10, 128-141.
34.
Jöreskog, K. G., & Sörbom, D. (1981). Analysis of linear structural relationships by maximum likelihood and least squares methods (Research Report No. 81-8). Uppsala, Sweden: University of Sweden.
35.
Jöreskog, K. G., & Sörbom, D. (1996). LISREL 8: User’s reference guide. Chicago: Scientific Software International.
36.
Kahn, J. H. (2006). Factor analysis in counseling psychology research, training, and practice: Principles, advances, and applications. The Counseling Psychologist, 34, 684-718.
37.
Kaplan, D. (2000). Structural equation modeling: Foundations and extensions. Newbury Park, CA: Sage.
38.
Kline, R. B. (1998). Principles and practice of structural equation modeling. New York: Guilford.
39.
Kline, R. B. (2005). Principles and practice of structural equation modeling (2nd ed.). New York: Guilford.
40.
Lent, R. W. (2005). A social cognitive view of career development and counseling. In S. D. Brown & R. W. Lent (Eds.), Career development and counseling: Putting theory and research to work (pp. 101-127). New York: John Wiley.
41.
Lent, R. W., Brown, S. D., & Gore, P. A. (1997). Discriminant and predictive validity of academic self-concept, academic self-efficacy, and mathematics-specific self-efficacy. Journal of Counseling Psychology, 44, 307-315.
42.
Lent, R. W., Brown, S. D., & Hackett, G. (1994). Toward a unifying social cognitive theory of career and academic interest, choice, and performance. Journal of Vocational Behavior, 45, 79-122.
43.
Lent, R. W., Lopez, F. G., Brown, S. D., & Gore, P. A. (1996). Latent structure of the sources of mathematics self-efficacy. Journal of Vocational Behavior, 49, 292-308.
44.
Long, B. C. (1998). Coping with workplace stress: A multiple-group comparison of female managers and clerical workers. Journal of Counseling Psychology, 45, 65-78.
45.
Long, B. C., Kahn, S. E., & Schutz, R. W. (1992). Causal model of stress and coping: Women in management. Journal of Counseling Psychology, 39, 227-239.
46.
MacCallum, R. C., & Austin, J. T. (2000). Applications of structural equation modeling in psychological research. Annual Review of Psychology, 51, 201-226.
47.
MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure models. Psychological Methods, 1, 130-149.
48.
Marsh, H. W., Hau, K.-T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler’s (1999) findings. Structural Equation Modeling, 11, 320-341.
49.
Martens, M. P. (2005). The use of structural equation modeling in counseling psychology research. The Counseling Psychologist, 33, 269-298.
50.
Martens, M. P., & Hasse, R. F. (in press [TCP special issue, part 2]). Advanced applications of structural equation modeling in counseling psychology research. The Counseling Psychologist, 34.
51.
Mathieu, J. E., & Farr, J. L. (1991). Further evidence for the discriminant validity of measures of organizational commitment, job involvement, and job satisfaction. Journal of Applied Psychology, 76, 127-133.
52.
McDonald, R. P., & Ho, M.-H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7, 64-82.
53.
Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.
54.
Mulaik, S. A., & Millsap, R. E. (2000). Doing the four-step right. Structural Equation Modeling, 7, 36-73.
55.
Muthén, L. K., & Muthén, B. O. (1998-2004). Mplus user’s guide (3rd ed.). Los Angeles: Muthén & Muthén.
56.
Quintana, S. M., & Maxwell, S. E. (1999). Implications of recent developments in structural equation modeling for counseling psychology. The Counseling Psychologist, 27, 485-527.
57.
Quintana, S. M., & Minami, T. (in press [TCP special issue, part 2]). Guidelines for meta-analyses of counseling psychology research. The Counseling Psychologist, 34.
58.
Rubin, D. B. (1976). Inference and missing data. Biometrika, 61, 581-592.
59.
Russell, D. W., Kahn, J. H., Spoth, R., & Altmaier, E. M. (1998). Analyzing data from experimental studies: A latent variable structural modeling approach. Journal of Counseling Psychology, 45, 18-29.
60.
SAS Institute. (2000). SAS/ETS software: Changes and enhancements (Release 8.1). Cary, NC: Author.
61.
Satorra, A., & Bentler, P. (1994). Corrections to test statistics and standard errors on covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis (pp. 399-419). Thousand Oaks, CA: Sage.
62.
Schumaker, R. E., & Lomax, R. G. (2004). A beginner’s guide to structural equation modeling (2nd ed.). Mahwah, NJ: Lawrence Erlbaum.
63.
Sherry, A. (2006). Discriminant analysis in counseling psychology research. The Counseling Psychologist, 34, 661-683.
64.
Steiger, J. H. (1990). Structural model evaluation and modification: An internal estimation approach. Multivariate Behavioral Research, 25, 173-180.
65.
Steiger, J. H, (2001). Driving fast in reverse: The relationship between software development, theory, and education in structural equation modeling. Journal of the American Statistical Association, 96, 331-338.
66.
Steiger, J. H., & Lind, J. C. (1980, May). Statistically based tests for the number of common factors. Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.
67.
Tracey, T. J. G. (2002). Development of interests and competency beliefs: A 1-year longitudinal study of fifth-to eighth-grade students using the ICA-R and structural equation modeling. Journal of Counseling Psychology, 49, 148-163.
68.
Tylka, T. L., & Subich, L. M. (2004). Examining a multidimensional model of eating disorder symptomatology among college women. Journal of Counseling Psychology, 51, 314-328.
69.
Wei, M., Heppner, P. P., & Mallinckrodt, B. (2004). Perceived coping as a mediator between attachment and psychological distress: A structural equation modeling approach. Journal of Counseling Psychology, 50, 438-447.
70.
Worthington, R. L., & Whittaker, T. A. (in press [TCP special issue, part 2]). Scale development research: A content analysis and recommendations for best practices. The Counseling Psychologist, 34.
71.
Yuan, K.-H., & Bentler, P. M. (1998). Normal theory based test statistics in structural equation modeling. British Journal of Mathematical and Statistical Psychology, 51, 289-309.
